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An algorithm to check if a number is an Extra Perfect Number (it has the same first and last bits) in javascript

This may seem obvious, but what is exactly is an extra perfect number? I need to write an algorithm to find extra perfect for a given n, from 1 thru n. Unfortunately, I can't seem to wrap my mind around the question's wording. These are the examples given:
extraPerfect(3) ==> return {1,3}
extraPerfect(7) ==> return {1,3,5,7}
Task:
Given a positive integer N, return the extra perfect numbers in range from 1 to N.
A number is called Extra Perfect Number if it has the same first and last bits (set bits).
Notes:
Only positive integers will be passed.
The returned vector/list should contain the extra perfect numbers in
ascending order (from lowest to highest).
Example #1
extraPerfect(3) ==> return {1,3}
Explanation:
(1)10 = (1)2
First and last bits as set bits.
(3)10 = (11)2
First and last bits as set bits.
Example #2
extraPerfect(7) ==> return {1,3,5,7}
Explanation:
(5)10 = (101)2
First and last bits as set bits.
(7)10 = (111)2
First and last bits as set bits.

It seems to me that an extra perfect number is simply an odd number as, in base 2, it will always start and end with a 1, whereas an even number will always start with a 1 but end with a 0.

Ah now I see I was wrong because I thought it is all about palindroms. However I hope it can be still helpful. That's the code for palindroms in section between 1 to prompt's value.
var exns = (function(){
function dec2bin(dec){
return (dec >>> 0).toString(2);
}
function isEXN(num){
var con = dec2bin(num); // 11011 = 3 + 24 = 27
var accurate = Math.ceil(con.length/2); // 5/2 = 3
var lenmin = con.length-1;
for(var i = 0; i < accurate; i++){
if(con.charAt(i) !== con.charAt(lenmin-i))
return false;
}
return true;
}
var max = parseInt(prompt("Numbers from 1 to ...?"));
var exns = [];
if(!isNaN(max)){
for(var i = 1; i<=max; i++){
if(isEXN(i))
exns.push(i);
}
}
return exns;
})();
Exns should contain array with values.

It looks like extraPerfect should return a list of all numbers less than the argument which have the same first and last digit after converting the decimal argument to binary.
For example:
Decimal - Binary
1 - 1
2 - 10
3 - 11
4 - 100
5 - 101
6 - 110
7 - 111
You'll notice the bold values have the same first and last binary digits.
Some pseudo-code might look like:
function extraPerfect( n ){
var perfects = [];
for(i=0; i<n; i++){
var binary = toBinary(i);
if(binary[0] === binary[binary.length]){
perfects.push(i);
}
}
return perfects;
}
You could pull an algorithm form the pseudo-code.

A Perfect Number is equal to the sum of its positive divisors.
function perfect(num){
for(var i=1,n=0; i<num; i++){
if(num % i === 0){
n += i;
}
}
return n === num;
}
console.log(perfect(6));
console.log(perfect(7));
console.log(perfect(28));
console.log(perfect(8127));
console.log(perfect(8128));

How can I check that a bit is set (without bitwise operation)?

Looking at the int 44 — I need Math.CEIL (log(2) 44) of binary places to represent 44.
(answer is 6 places)
6 places :
___ ___ ___ ___ ___ ___
32 16 8 4 2 1
But how can I check that (for example) the bit of 8 is checked or not ?
A simple solution will be do to :
((1<<3) & 44)>0 so this will check if the bit is set.
But please notice that behind the scenes the computer translates 44 to its binary representation and just check if bit is set via bitwise operation.
Another solution is just to build the binary myself via toString(2) or mod%2 in a loop
Question
Mathematically Via which formula, I can test if n'th bit is set ?
(I would prefer a non loop operation but pure single math phrase)

Divide by the value of the bit that you want to check
and test if the first bit is set (this can be tested with x mod 2 == 1)
Math expression:
floor(value/(2^bitPos)) mod 2 = 1
As JS function:
function isSet(value, bitPos) {
var result = Math.floor(value / Math.pow(2, bitPos)) % 2;
return result == 1;
}
Note: bitPos starts with 0 (bit representing the nr 1)

The 'bit' (actually any base) value of an indexed number index in a value val in base base can in general be calculated as
val = 1966;
index = 2;
base = 10;
alert (Math.floor(val/Math.pow(base,index)) % base);
result: 9
val = 44;
index = 3;
base = 2;
alert (Math.floor(val/Math.pow(base,index)) % base);
result: 1 (only 0 and 1 are possible here – the range will always be 0..base-1).
The combination of Math.floor (to coerce to an integer in Javascript) and Math.pow is kind of iffy here. Even in integer range, Math.pow may generate a floating point number slightly below the expected 'whole' number. Perhaps it is safer to always add a small constant:
alert (Math.floor(0.1+val/Math.pow(base,index)) % base);

You can simply check if the bit at the position is set to 1.
function isBitSet(no, index) {
var bin = no.toString(2);
// Convert to Binary
index = bin.length - index;
// Reverse the index, start from right to left
return bin[index] == 1;
}
isBitSet(44, 2); // Check if second bit is set from left
DEMO

How to format clean numbers so 1000 appear as 1.000,00 [duplicate]

This question already has answers here:
How to format a number with commas as thousands separators?
(50 answers)
Closed 9 years ago.
I currently have some clean numbers like:
1, 10, 100, 1000, 10000 etc...
Im looking to format these numbers, so they appear as:
1,00
10,00
100,00
1.000,00
10.000,00
I played around with n.toFixed(2); but didn't seem to support the formatting im looking for.
Any ideas?

Check out Intl.NumberFormat(), no fancy pants plugins needed. Cross-platform support.
var number = 3500;
alert(new Intl.NumberFormat().format(number));
Will pop up '3,500'

If you want a simple function to do the job, the following may suit:
// Format a number n using:
// p decimal places (two by default)
// ts as the thousands separator (comma by default) and
// dp as the decimal point (period by default).
//
// If p < 0 or p > 20 results are implementation dependent.
function formatNumber(n, p, ts, dp) {
var t = [];
// Get arguments, set defaults
if (typeof p == 'undefined') p = 2;
if (typeof ts == 'undefined') ts = ',';
if (typeof dp == 'undefined') dp = '.';
// Get number and decimal part of n
n = Number(n).toFixed(p).split('.');
// Add thousands separator and decimal point (if requied):
for (var iLen = n[0].length, i = iLen? iLen % 3 || 3 : 0, j = 0; i <= iLen; i+=3) {
t.push(n[0].substring(j, i));
j = i;
}
// Insert separators and return result
return t.join(ts) + (n[1]? dp + n[1] : '');
}
//*
console.log(formatNumber(
1234567890.567, // value to format
4, // number of decimal places
'.', // thousands separator
',' // decimal separator
)); // result: 1.234.567.890,5670
//*/
console.log(formatNumber(
123.567, // value to format
1 // number of decimal places
)); // result: 123.6
console.log(formatNumber(
'123.567', // value to format
0 // number of decimal places
)); // result: 123.6
console.log(formatNumber(
123, // value to format
0 // number of decimal places
)); // result: 123
console.log(formatNumber(
13, // value to format
2 // number of decimal places
)); // result: 13.00
console.log(formatNumber(
0 // value to format
// number of decimal places
)); // result: 0.00
console.log(formatNumber(
// value to format
// number of decimal places
)); // result: NaN
Sorry, no fancy regular expressions or slice/splice array stuff, just POJS that works.

You can do it like this:
var nb='1000000000';
var result = nb.replace(/(?:(^\d{1,3})(?=(?:\d{3})*$)|(\d{3}))(?!$)/mg, '$1$2.')+',00';

There is no built-in methods for formatting numbers in JS. You can use autoNumeric for this. http://www.decorplanit.com/plugin/

I don't know what your situation is, but i'd like to use angularJS.
It serves exactly what you are looking for and there are more extra dynamic formatting.
UPDATE: Specifically look into Localization functionality. It even serves pluralization if you need it.

jQuery: why is an integer being added to a variable like a string?

So I'm trying to take the variable that increments in a for statement, and add an integer to it... but for some reason, it's adding the integer as though it were a string; other operations like subtraction or multiplication work as expected.
Why is this happening? Edit: I've added the whole function; the problem in question is where I try to add 2 to the variable x.
What confuses me is that I'm able to use x no problem, in an .eq() object for example...
$(function() {
$('textarea').bind('paste', function (e){
inputGroup = $(this).parent();
var ob = $(this);
if (e.type == 'paste'){
setTimeout(function(){
var data = ob.val();
var tabbed = data.replace(/\n/g, "\t");
var cells = tabbed.split("\t");
for(var x in cells) {
foo = x + 2;
alert(foo);
$(inputGroup).find('input').eq(x).val(cells[x]);
}
}, 1);
}
});
});

Why is this happening?
Because x is a string that just looks like a number. Cast to Number first and you'll get the result you expect:
"1" + 2 = "12"
Number("1") + 2 = 3
EDIT : Now that I see you are using split to turn a string into an array, your problem is definitely that you are concatenating strings. Cast to Number first, and your problem is solved.
Yes other arithmetic operations will work, since they will implicitly cast the operands to Numbers. Confusingly, "2" * 3 will in fact evaluate to the integer 6. Welcome to Javascript.
-tjw

Without more code, specifically the initialization of cells, I can't tell you the exact reason. But you can simply call parseInt() on x to turn it into an integer for addition
for(var x in cells) {
foo = parseInt(x, 10) + 2;
$(inputGroup).find('input').eq(foo).val(cells[x]);
}

Because + is a String concatenation but there is no equivalent String method for * or / so when using those it cast the value as a Number. Just cast x as an integer:
for(var x in cells) {
foo = parseInt(x, 10) + 2;
$(inputGroup).find('input').eq(foo).val(cells[x]);
}
The 10 in parseInt is saying to use a base 10 number system (as opposed to hex 16, e.g.).

As others have mentioned, x is a string. That's why.
There's a nice trick for casting strings as numbers in JavaScript that hasn't been mentioned though:
for(var x in cells) {
// Without the "var" here, you're setting a global
// variable during each loop iteration.
var foo = +x + 2;
$(inputGroup).find('input').eq(foo).val(cells[x]);
}

Javascript: Comparing two float values [duplicate]

This question already has answers here:
Javascript float comparison
(2 answers)
Closed 6 months ago.
I have this JavaScript function:
Contrl.prototype.EvaluateStatement = function(acVal, cfVal) {
var cv = parseFloat(cfVal).toFixed(2);
var av = parseFloat(acVal).toFixed(2);
if( av < cv) // do some thing
}
When i compare float numbers av=7.00 and cv=12.00 the result of 7.00<12.00 is false!
Any ideas why?

toFixed returns a string, and you are comparing the two resulting strings. Lexically, the 1 in 12 comes before the 7 so 12 < 7.
I guess you want to compare something like:
(Math.round(parseFloat(acVal)*100)/100)
which rounds to two decimals

Compare float numbers with precision:
var precision = 0.001;
if (Math.abs(n1 - n2) <= precision) {
// equal
}
else {
// not equal
}
UPD:
Or, if one of the numbers is precise, compare precision with the relative error
var absoluteError = (Math.abs(nApprox - nExact)),
relativeError = absoluteError / nExact;
return (relativeError <= precision);

The Math.fround() function returns the nearest 32-bit single precision float representation of a Number.
And therefore is one of the best choices to compare 2 floats.
if (Math.fround(1.5) < Math.fround(1.6)) {
console.log('yes')
} else {
console.log('no')
}
>>> yes
// More examples:
console.log(Math.fround(0.9) < Math.fround(1)); >>> true
console.log(Math.fround(1.5) < Math.fround(1.6)); >>> true
console.log(Math.fround(0.005) < Math.fround(0.00006)); >>> false
console.log(Math.fround(0.00000000009) < Math.fround(0.0000000000000009)); >>> false

Comparing floats using short notation, also accepts floats as strings and integers:
var floatOne = 2, floatTwo = '1.456';
Math.floor(floatOne*100) > Math.floor(floatTwo*100)
(!) Note: Comparison happens using integers. What actually happens behind the scenes: 200 > 145
Extend 100 with zero's for more decimal precision. For example use 1000 for 3 decimals precision.
Test:
var floatOne = 2, floatTwo = '1.456';
console.log(Math.floor(floatOne*100), '>', Math.floor(floatTwo*100), '=', Math.floor(floatOne*100) > Math.floor(floatTwo*100));

Comparing of float values is tricky due to long "post dot" tail of the float value stored in the memory. The simplest (and in fact the best) way is: to multiply values, for reducing known amount of post dot digits to zero, and then round the value (to rid of the tail).
Obviously both compared values must be multiplied by the same rate.
F.i.: 1,234 * 1000 gives 1234 - which can be compared very easily. 5,67 can be multiplied by 100, as for reducing the float comparing problem in general, but then it couldn't be compared to the first value (1,234 vel 1234). So in this example it need to be multiplied by 1000.
Then the comparition code could look like (in meta code):
var v1 = 1.234;
var v2 = 5.67;
if (Math.round(v1*1000) < Math.round(v2*1000)) ....